You simply call bell services to store your unnecessary luggage and enjoy your day in whatever fashion you wish. You won't have access to your room with your key, but you are able to come and go from the common areas of the concierge building until you leave the resort OR midnight, whichever comes first!
You are also able to store a small bag or two at the concierge desks in the event you want to swim, freshen up prior to your flight, etc. The third floor restroom is available to you to change for the pool, freshen up, etc.
The concierge service is available to you the entire day. You are able to avail yourselves of the lounge area for snacks, sodas, evening, and/or dessert service as well.
While we don't usually fly out at the end of our final day (we transfer to the Hyatt at the airport), we do make full use of our final day by hitting parks, swimming, hanging in the lounge, dining at EPCOT, etc. The concierge staff is just as cordial to us the last day as they are on the first. Further, we inquired about all of this on our first stay--while late check-outs are not encouraged and during peak or regular season, rarely available--the staff has never discouraged us from feeling at home until we leave WDW property.
Just an FYI, this also applied to all of the concierge services we've sampled. Have a great trip!